CN102721374B - Planar sub-aperture splicing method based on weighted least square method - Google Patents
Planar sub-aperture splicing method based on weighted least square method Download PDFInfo
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Abstract
The invention discloses a planar sub-aperture splicing method based on a weighted least square method. The planar sub-aperture splicing method comprises a method for calculating weight values of overlapped regions in the sub-aperture splicing process, wherein the method can correctly reflect the confidence levels of the overlapped regions in the sub-aperture splicing process, the weight values of the regions with high noise are small, and the weight values of the regions with low noise are large; and the quadratic sum of the weighted residual errors of the overlapped regions is required to be minimal when the tilt coefficients and the translation coefficients of the sub-apertures are calculated. According to the planar sub-aperture splicing method, the weight values of the different overlapped regions are calculated and the tilt coefficients and the translation coefficients of the sub-apertures are calculated by the weighted least square method, so that the influence of the noise on the sub-aperture splicing process is inhibited and the planar sub-aperture splicing precision is improved.
Description
Technical field
The invention belongs to optic test field, relate generally to a kind of plane sub-aperture stitching method based on weighted least-squares method.
Background technology
Along with scientific and technical development, heavy-caliber optical system uses more and more wider in the field such as Aeronautics and Astronautics, military affairs.Traditional optical detecting method needs a bigbore standard component in the time detecting heavy caliber face shape, and bigbore standard component is manufactured processing difficulties, and the spatial resolution of testing result is subject to the restriction of detector resolution.Sub-aperture stitching measuring method, by multiple sub-aperture plane graphic data with certain overlapping region are spliced, has been removed heavy caliber standard component from, has reduced cost, has improved spatial resolution.
Traditional sub-aperture stitching method is all first to obtain inclination, the translation coefficient in each sub-aperture according to overlapping region phase error inconsistency minimum principle (least square method), then each sub-aperture tilt quantity, translational movement are compensated, thereby obtain full aperture face shape.
Mark A.Schmucker, Joanna Schmit, the joining method in the sub-aperture of a kind of plane has been proposed at " US 5991461 ", its basic thought is that each sub-aperture is spliced according to certain priority orders, the regions priority that noise is little is high, to splicing order sensitivity, there are cumulative errors in the method.
QED company of the U.S. has proposed droop error, translation error, the reference surface error in the each sub-aperture of a kind of while Optimization Compensation, the method for distortion error at " US 6956657 ", and the method is not considered the impact of noise on splicing.
In actual measurement, each sub-aperture, except introducing because mechanical hook-up moves the droop error and translation error of bringing, is also subject to the impact of the noise sources such as vibration in CCD, light source, environment, temperature, air turbulence, introduces noise.For reducing the impact of these noises on sub-aperture stitching, propose a kind of sub-aperture stitching method based on weighted least-squares method herein, and proposed a kind of method of asking for weights.
Summary of the invention
The object of the invention is in order to overcome the deficiencies in the prior art, a kind of plane sub-aperture stitching method based on weighted least-squares method has been proposed, suppress the impact of noise region in sub-aperture stitching, for the splicing precision that improves sub-aperture stitching provides a kind of means.
To achieve these goals, as shown in Figure 2, concrete steps are as follows for the technical solution adopted in the present invention:
(1), according to the face graphic data in sub-aperture, calculate the weights W of each overlapping region
l, m, x, y.Weights W
l, m, x, yl, m, x, the function of y, the weights of pixel (x, y) in the overlapping region between the expression sub-aperture of l and the sub-aperture of m.The present invention requires weights W
l, m, x, ycan answer the confidence level size of overlapping region in splicing by reacting phase, the region weights that noise is large are little, and the region weights that noise is little are large.In measurement, be subject to the feature of noise according to each sub-aperture plane graphic data, by weights W
l, m, x, ybe divided into first kind weights p
l, m, x, ywith Equations of The Second Kind weights q
l, m, first kind weights p
l, m, x, yreact sub-aperture plane shape and be subject to the impact of discrete point noise, Equations of The Second Kind weights q
l, mreact sub-aperture plane shape and be subject to the impact of regional noise.And then these two classes weights are multiplied each other and obtain weights W
l, m, x, y, its concrete computing method are as follows:
A) choose the sub-aperture of h as reference field (a
h=0, b
h=0, c
h=0, h=1 ... any one number in M, M represents total sub-aperture number), adopt least square method (the quadratic sum ε minimum of overlapping region residual error), solve the directions X inclination factor a in each sub-aperture
j, Y-direction inclination factor b
jwith axial translation coefficient c
j, method is shown below:
Wherein, (x
i, y
i) be the coordinate of i pixel in the overlapping region in the sub-aperture of l and the sub-aperture of m, f
l(x
i, y
i) be pixel (x
i, y
i) face graphic data in l sub-aperture, f
m(x
i, y
i) be pixel (x
i, y
i) face graphic data in m sub-aperture, a
lbe the directions X inclination factor in l sub-aperture, b
lbe the Y-direction inclination factor in l sub-aperture, c
lbe l the axial translation coefficient in sub-aperture, a
mbe the directions X inclination factor in m sub-aperture, b
mbe the Y-direction inclination factor in m sub-aperture, c
mbe m the axial translation coefficient in sub-aperture, N
l, mbe the pixel sum of the overlapping region in the sub-aperture of I and the sub-aperture of m, ε is the quadratic sum of overlapping region residual error, and M represents total sub-aperture number, j=1,2 ... M, represents sub-aperture sequence number, i=1, and 2 ..., N
l, m, be the pixel sequence number in the overlapping region in the sub-aperture of l and the sub-aperture of m.
B) according to the directions X inclination factor a that solves each sub-aperture in a)
j, Y-direction inclination factor b
j, axial translation coefficient c
j, calculate the quadratic sum ε of each overlapping region residual error
l, m, method is shown below:
Wherein, ε
l, mrepresent the residual error quadratic sum of the overlapping region in the sub-aperture of l and the sub-aperture of m.
C) according to the ε obtaining in b)
l, m, rule of thumb selected threshold parameter k, calculates first kind weights p
l, m, x, y, be shown below:
v
l,m，x，y＝f
l(x,y)-f
m(x,y)+a
lx+b
ly+c
l-a
mx-b
my-c
m
Wherein v
l, m, x, yrepresent the residual error of pixel (x, y) in the overlapping region in the sub-aperture of l and the sub-aperture of m.
D) according to ε b) obtaining
l, m, calculate Equations of The Second Kind weights q
l, m, be shown below:
E) by p c) calculating
l, m, x, ywith d) in calculate calculate q
l, mmultiply each other, obtain weights W
l, m, x, y, be shown below:
W
l，m，x，y＝p
l，m，x，y·q
l,m。
(2) according to the weights W calculating in (1)
l, m, x, y, adopt weighted least-squares method (to make the weighting residual error quadratic sum minimum of each overlapping region
), calculate the inclination factor of the directions X of each sub-aperture under weighting
the inclination factor of the Y-direction under weighting
with the axial translation coefficient under weighting
Wherein,
for the directions X inclination factor in the l under weighting sub-aperture,
for the Y-direction inclination factor in the l under weighting sub-aperture,
for the l under weighting the axial translation coefficient in sub-aperture,
for the directions X inclination factor in the m under weighting sub-aperture,
for the Y-direction inclination factor in the m under weighting sub-aperture,
for the m under weighting the axial translation coefficient in sub-aperture,
for the weighting residual error quadratic sum of each overlapping region.
(3) according to the inclination factor of the directions X under the weighting in the each sub-aperture drawing in (2)
the inclination factor of the Y-direction under weighting
with the axial translation coefficient under weighting
calculate full aperture face graphic data f (x, y), method is shown below:
Brief description of the drawings
Fig. 1 is the measurement mechanism structural representation in the embodiment of the present invention;
Fig. 2 is the splicing process flow diagram that the present invention realizes;
Fig. 3 is the measurement scheme in the embodiment of the present invention.
Embodiment
For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing, enforcement of the present invention is further described.
The present embodiment is taking the parallel plane sub-aperture stitching in 9 apertures as example.
Fig. 1 is measurement mechanism structural representation of the present invention, comprises Feisuo interferometer 101, two-dimension translational platform 102, numerical control device 103, computing machine 104, tested plane 105.Numerical control device 103 is connected with two-dimension translational platform 102, to control the motion of two-dimension translational platform 102; Computing machine 104 is connected with Feisuo interferometer 101 with numerical control device 103 respectively, for sending and receive information to numerical control device 103 and Feisuo interferometer 101.
Adopt measurement mechanism as shown in Figure 1 to measure tested plane.First adjust light path, the test beams that interferometer 101 sends can be arrived in tested plane 105, test beams interferes with the light beam returning through the reference surface of interferometer 101 after tested plane 105 is returned, and can realize the measurement to tested plane 105; Adopt measurement scheme as shown in Figure 3, full aperture is divided into 9 sub-apertures, and records the positional information in each sub-aperture; Computing machine 104 sends the positional information in the 1st sub-aperture to numerical control device 103, and numerical control device 103 receives that positional information rear drive two-dimension translational platform 102 moves to corresponding position, and returns to the information having moved to computing machine 104; Computing machine 104 is received after the information that numerical control device 103 returns, and sends the information of measuring tested plane 105 to Feisuo interferometer 101; Feisuo interferometer 101 receives after the information of computing machine 104, measures tested plane 105, obtains the face graphic data f in the 1st sub-aperture
1(x, y), and return to computing machine 104 information that the 1st sub-aperture plane shape measurement completes; Computing machine 104 receives after the information that Feisuo interferometer 101 returns, then sends the positional information in the 2nd sub-aperture to numerical control device 103, so repeats, until obtain the face graphic data f in 9 sub-apertures
j(x, y), j=1,2 ... 9.
As shown in Figure 2, concrete steps are as follows for the flow process of the joining method based on weighted least-squares method:
(1) first according to the face graphic data f in each sub-aperture
j(x, y), calculates the weights W of each overlapping region
l, m, x, y.Weights W
l, m, x, yl, m, x, the function of y, the weights of pixel (x, y) in the overlapping region between the expression sub-aperture of l and the sub-aperture of m.The present invention requires weights W
l, m, x, ycan answer the confidence level size of overlapping region in splicing by reacting phase, the region weights that noise is large are little with a low credibility, and the region weights that noise is little are with a high credibility greatly.In measurement, be subject to the feature of noise according to each sub-aperture plane graphic data, by weights W
l, m, x, ybe divided into first kind weights p
l, m, x, ywith Equations of The Second Kind weights q
l, m, first kind weights p
l, m, x, y, react sub-aperture plane shape and be subject to the impact of discrete point noise, Equations of The Second Kind weights q
l, mreact sub-aperture plane shape and be subject to the impact of regional noise.And then by this two classes weights combination, obtain weights W
l, m, x, y, concrete calculation procedure is as follows:
A) choose the 1st sub-aperture as reference field (a
1=0, b
1=0, c
1=0), adopt the least square method quadratic sum ε minimum of overlapping region residual error (, make), solve the directions X inclination factor a in each sub-aperture
j, Y-direction inclination factor b
jwith axial translation coefficient c
j, method is shown below:
Wherein, (x
i, y
i) be the coordinate of i pixel in the overlapping region in the sub-aperture of l and the sub-aperture of m, f
l(x
i, y
i) be pixel (x
i, y
i) face graphic data in l sub-aperture, f
m(x
i, y
i) be pixel (x
i, y
i) face graphic data in m sub-aperture, a
lbe the directions X inclination factor in l sub-aperture, b
lbe the Y-direction inclination factor in l sub-aperture, c
lbe l the axial translation coefficient in sub-aperture, a
mbe the directions X inclination factor in m sub-aperture, b
mbe the Y-direction inclination factor in m sub-aperture, c
mbe m the axial translation coefficient in sub-aperture, M represents total sub-aperture number, and in the present embodiment, M is 9, N
l, mbe the pixel sum of the overlapping region in the sub-aperture of I and the sub-aperture of m, ε is the quadratic sum of overlapping region residual error, j=1,2 ... 9, represent sub-aperture sequence number, i=1,2 ..., N
l,mit is the pixel sequence number in the overlapping region in the sub-aperture of l and the sub-aperture of m.
B) according to the directions X inclination factor a that solves each sub-aperture in a)
j, Y-direction inclination factor b
j, axial translation coefficient a
j, calculate the quadratic sum ε of each overlapping region residual error
l, m, method is shown below:
Wherein, ε
l, mrepresent the residual error quadratic sum of the overlapping region in the sub-aperture of l and the sub-aperture of m.
C) according to the ε obtaining in b)
l, m, rule of thumb selected threshold parameter k=3, calculates first kind weights p
l, m, x, y, be shown below:
v
l,m，x，y＝f
l(x,y)-f
m(x,y)+a
lx+b
ly+c
l-a
mx-b
my-c
m
Wherein v
l, m, x, yrepresent the residual error of pixel (x, y) in the overlapping region in the sub-aperture of l and the sub-aperture of m.
D) according to ε a) obtaining
l, m, calculate Equations of The Second Kind weights q
l, m, be shown below:
E) by p c) calculating
l, m, x, ywith d) in calculate calculate q
l, mmultiply each other, obtain weights W
l, m, x, y, be shown below:
W
l，m，x，y＝p
l，m，x，y·q
l,m
(2) according to the weights W calculating in (1)
l, m, x, y, adopt weighted least-squares method (to make the weighting residual error quadratic sum minimum of each overlapping region
), solve the inclination factor of the directions X under the weighting in each sub-aperture
the inclination factor of the Y-direction under weighting
with the axial translation coefficient under weighting
Wherein,
for the directions X inclination factor in the l under weighting sub-aperture,
for the Y-direction inclination factor in the l under weighting sub-aperture,
for the l under weighting the axial translation coefficient in sub-aperture,
for the directions X inclination factor in the m under weighting sub-aperture,
for the Y-direction inclination factor in the m under weighting sub-aperture,
for the m under weighting the axial translation coefficient in sub-aperture,
for the weighting residual error quadratic sum of each overlapping region.
(3) according to the inclination factor of the directions X under the weighting in the each sub-aperture drawing in (2)
the inclination factor of the Y-direction under weighting
with the axial translation coefficient under weighting
calculate full aperture face graphic data f (x, y), method is shown below:
Claims (5)
1. the plane sub-aperture stitching method based on weighted least-squares method, is characterized in that step is as follows:
(1) according to the face graphic data f in each sub-aperture
j(x, y), calculates the weights W of each overlapping region
l, m, x, y;
(2) according to the weights W calculating in step (1)
l, m, x, y, adopt weighted least-squares method, make the weighting residual error quadratic sum of each overlapping region
minimum, calculates the inclination factor of the directions X under the weighting in each sub-aperture
the inclination factor of the Y-direction under weighting
with translation coefficient axial under weighting
j=1,2 ..., M, represents j sub-aperture, M represents total sub-aperture number, is shown below:
Wherein, (x
i, y
i) be the coordinate of i pixel in the overlapping region in the sub-aperture of l and the sub-aperture of m, f
l(x
i, y
i) be pixel (x
i, y
i) face graphic data in l sub-aperture, f
m(x
i, y
i) be pixel (x
i, y
i) face graphic data in m sub-aperture,
for the directions X inclination factor in the l under weighting sub-aperture,
for the Y-direction inclination factor in the l under weighting sub-aperture,
for the l under weighting the axial translation coefficient in sub-aperture,
for the directions X inclination factor in the m under weighting sub-aperture,
for the Y-direction inclination factor in the m under weighting sub-aperture,
for the m under weighting the axial translation coefficient in sub-aperture,
for the weighting residual error quadratic sum of each overlapping region, N
l,mbe the pixel sum of the overlapping region in the sub-aperture of l and the sub-aperture of m, i=1,2 ..., N
l,m, be the pixel sequence number in the overlapping region in the sub-aperture of l and the sub-aperture of m;
(3) according to the inclination factor of the directions X under the weighting in the each sub-aperture drawing in step (2)
the inclination factor of the Y-direction under weighting
with the axial translation coefficient under weighting
calculate full aperture face graphic data f (x, y), method is shown below:
。
2. the plane sub-aperture stitching method based on weighted least-squares method according to claim 1, is characterized in that: the weights W of overlapping region
l, m, x, yl, m, x, the function of y, W
l, m, x, ycan reflect the confidence level size of corresponding overlapping region in splicing, the region weights that noise is large are little, and the region weights that noise is little are large.
3. the plane sub-aperture stitching method based on weighted least-squares method according to claim 1, is characterized in that: the weights W of the each overlapping region in described step (1)
l, m, x, ythe feature that is subject to noise according to each sub-aperture plane graphic data in measurement, is divided into first kind weights p
l, m, x, ywith Equations of The Second Kind weights q
l,m, first kind weights p
l, m, x, yreflect that sub-aperture plane shape is subject to the impact of discrete point noise, Equations of The Second Kind weights q
l,mreflect that sub-aperture plane shape is subject to the impact of regional noise; And then these two classes weights are multiplied each other, obtain weights W
l, m, x, y, its concrete computing method are as follows:
A) adopt least square method, make the quadratic sum ε minimum of overlapping region residual error, solve the directions X inclination factor a in each sub-aperture
j, Y-direction inclination factor b
jwith axial translation coefficient c
j, j=1,2 ..., M, represents j sub-aperture, and M represents total sub-aperture number, and method is shown below:
B) solve directions X inclination factor a according in (a)
j, Y-direction inclination factor b
j, axial translation coefficient c
j, calculate the quadratic sum ε of each overlapping region residual error
l,m, method is shown below:
C) according to the ε obtaining in b)
l,m, rule of thumb selected threshold parameter k, calculates first kind weights p
l, m, x, y, be shown below:
v
l,m,x,y＝f
l(x,y)-f
m(x,y)+a
lx+b
ly+c
l-a
mx-b
my-c
m
D) according to ε b) obtaining
l,m, calculate Equations of The Second Kind weights q
l,m, be shown below:
E) by p c) calculating
l, m, x, ywith d) in calculate calculate q
l,mmultiply each other, obtain weights W
l, m, x, y, be shown below:
W
l,m,x,y＝p
l,m,x,y·q
l,m。
4. the plane sub-aperture stitching method based on weighted least-squares method according to claim 1, is characterized in that: described step (1) before, is first read in the face graphic data in the sub-aperture of measurement mechanism acquisition; Described measurement mechanism comprises Feisuo interferometer (101), two-dimension translational platform (102), numerical control device (103), computing machine (104), tested plane (105); Numerical control device (103) is connected with two-dimension translational platform (102), to control the motion of two-dimension translational platform (102); Computing machine (104) is connected with Feisuo interferometer (101) with numerical control device (103) respectively, for carrying out information interaction with numerical control device (103) and Feisuo interferometer (101).
5. the plane sub-aperture stitching method based on weighted least-squares method according to claim 4, it is characterized in that: the step of face graphic data that described measurement mechanism obtains sub-aperture is as follows: first adjust light path, the test beams that interferometer (101) sends can be arrived in tested plane (105), test beams interferes with the light beam returning through the reference surface of interferometer (101) after tested plane (105) is returned, and can realize the measurement to tested plane (105); Determine measurement scheme, and record the positional information in each sub-aperture; Computing machine (104) sends the positional information in the 1st sub-aperture to numerical control device (103), numerical control device (103) receives that positional information rear drive two-dimension translational platform 102 moves to corresponding position, and returns to the information having moved to computing machine (104); Computing machine (104) is received after the information that numerical control device (103) returns, and sends the information of measuring tested plane (105) to Feisuo interferometer (101); Feisuo interferometer (101) receives after the information of computing machine (104), measures tested plane (105), obtains the face graphic data f in sub-aperture
1(x, y), and return to computing machine (104) information that the 1st sub-aperture plane shape measurement completes; Computing machine (104) receives after the information that Feisuo interferometer (101) returns, then sends the positional information in the 2nd sub-aperture to numerical control device (103), so repeats, until obtain the face graphic data f in all sub-apertures
j(x, y).
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| CN105157572B (en) * | 2015-09-29 | 2017-09-12 | 西安交通大学 | A kind of off-centring error compensating method spliced for aspherical annular sub-aperture |
| CN105823430B (en) * | 2016-03-17 | 2018-10-12 | 南京理工大学 | Image Acquisition when visual field is less than flexible annular accessory size and joining method |
| CN105890541B (en) * | 2016-04-12 | 2018-04-17 | 中国科学院上海光学精密机械研究所 | A kind of high precision plane sub-aperture stitching detection method |
| CN107977939B (en) * | 2017-11-29 | 2021-11-16 | 浙江理工大学 | Reliability-based weighted least square phase unwrapping calculation method |
| CN110544207B (en) * | 2019-08-29 | 2023-04-28 | 中国人民解放军国防科技大学 | Sub-aperture data splicing method, system and medium for large-area microstructure morphology |
| CN111623957B (en) * | 2020-05-11 | 2022-03-25 | 中国科学院光电技术研究所 | Point cloud registration and splicing method for X-ray focusing lens splicing interference detection |
| CN114812428B (en) * | 2021-01-21 | 2023-09-01 | 中国科学院上海光学精密机械研究所 | Planar surface shape sub-aperture splicing interferometry device and measurement method |
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| US7136519B2 (en) * | 1999-12-30 | 2006-11-14 | Ade Corporation | Specimen topography reconstruction |
| CN101241000A (en) * | 2008-03-14 | 2008-08-13 | 中国人民解放军国防科学技术大学 | High steepness convex quadric aspherical aberration-free point Sub-Aperture Stitching measurement method |
| CN101419063A (en) * | 2008-10-30 | 2009-04-29 | 上海大学 | Cylindricity non-contact measurement method and system based on multi-diameter splicing technology |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7136519B2 (en) * | 1999-12-30 | 2006-11-14 | Ade Corporation | Specimen topography reconstruction |
| CN101241000A (en) * | 2008-03-14 | 2008-08-13 | 中国人民解放军国防科学技术大学 | High steepness convex quadric aspherical aberration-free point Sub-Aperture Stitching measurement method |
| CN101419063A (en) * | 2008-10-30 | 2009-04-29 | 上海大学 | Cylindricity non-contact measurement method and system based on multi-diameter splicing technology |
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